Abstract

We study the velocity-force (V-F) relation for a Brownian ratchet consisting of a linear rigid polymer growing against a diffusing barrier, acted upon by a opposing constant force (F). Using a careful mathematical analysis, we derive the V-F relations in the extreme limits of fast and slow barrier diffusion. In the first case, V depends exponentially on the load F, in agreement with the well-known formula proposed by Peskin, Odell and Oster (1993), while the relationship becomes linear in the second case. For a bundle of two filaments growing against a common barrier, equal sharing of load in the corresponding V-F relation is predicted by a mean-field argument in both limits. However, the scaling behaviour of velocity with the number of filaments is different for the two cases. In the limit of large D, the validity of the mean-field approach is tested, and partially supported by a detailed and rigorous analysis. Our principal predictions are also verified in numerical simulations.

Graphic abstract

中文翻译：

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重新审视线性聚合棘轮中的力-速度关系和负载分配：势垒扩散的影响

摘要

我们研究了布朗棘轮的速度-力 (VF) 关系，该棘轮由线性刚性聚合物组成，在扩散屏障上生长，并受到相反的恒定力 (F) 的作用。通过仔细的数学分析，我们得出了快速和慢速势垒扩散极限下的 VF 关系。在第一种情况下，V 与负载 F 成指数关系，这与 Peskin、Odell 和 Oster (1993) 提出的著名公式一致，而在第二种情况下，关系变为线性。对于生长在一个共同障碍物上的一束两根细丝，在相应的 VF 关系中负载的相等分配是由两个限制中的平均场参数预测的。然而，对于这两种情况，速度随灯丝数量的比例变化是不同的。在大 D 的范围内，平均场方法的有效性经过了测试，并得到了详细而严格的分析的部分支持。我们的主要预测也在数值模拟中得到验证。

图形摘要